Method of enhancing the bioavailability of a tocotrienol to a human for treating a disease or condition amenable to treatment with a tocotrienol, by administering a composition formulated for transmucosal delivery to the human. The composition contains at least one tocotrienol, and the disease or condition is selected from post-exercise muscle soreness, delayed onset muscle soreness, cardiac fibrosis, hypertension, inflammation, stroke, cancer, elevated cholesterol and/or triglycerides, baldness, hypertrophy and a condition resulting from radiation exposure.